When are two numerical polynomials relatively prime?

Let a and b be two polynomials having numerical coefficients. We consider t he question: When are a and b relatively prime? Since the coefficients of a and b are approximant, the question is the same as: When are two polynomia ls relatively prime, even after small perturbations of the coefficients? In this paper we provide a numeric parameter for determining whether two po lynomials are prime, even under small perturbations of the coefficients. Ou r methods rely on an inversion formula for Sylvester matrices to establish an effective criterion for relative primeness. The inversion formula can al so be used to approximate the condition number of a Sylvester matrix. (C) 1 998 Academic Press.